How to verify users

I run non profit for animals. Using wordpress for a site on the treatment of farm animals. This can be a rather controversial subject, and I cannot allow people to leave comments without some way of verifying if necessary who they are. Right now when people register it just asks for a user name and email address. What I need ( not to be published, but for my verification purposes if necessary ) is for a person to supply their real name , address and hopefully phone number on registering ..letting them know that these will not be used in any way other than for verification if required.
I apologize that I am not sure exactly what version of wordpress being used…was just installed a month or so ago. I am an old fart, and it was installed for me by someone else who could not determine a way to do as I need. It is being used at https://www.sadpig.info . If there is a way to do as I need and it is beyond me…(quite possible! ?? I will find someone to help if I can be told how. Fingers crossed!
Thank!
Barry